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Finite element solution of the Helmholtz equation with high wave number. II: The \(h-p\) version of the FEM. (English) Zbl 0884.65104
This paper is a continuation of an extensive investigation of the Galerkin finite element method (FEM) applied to the Helmholtz equation [cf. the authors, Comput. Math. Appl. 30, No. 9, 9-37 (1995; Zbl 0838.65108)]. Stability estimates are given for both the continuous and discrete spaces considered, together with an error analysis of the Galerkin FEM. Numerical illustrations are presented together with an analysis of the accuracy and the computational effort.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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